Why is the volume of a sphere V=4/3*pi*r^3? Here's a calculus proof using the disk method!

Why is the volume of a sphere V=4/3pir^3? Here's a calculus proof using the disk method!

Рет қаралды 10,408

2 ай бұрын

This tutorial covers why the sphere with radius r has the volume V=4/3*pi*r^3. We will prove this by using the disk method for the volume of a solid of revolution. This is an application of integration that you will learn in your Calculus 2 class.
Check out the volume of a cone proof 👉 • Why is the volume of a...
For the volume integral formulas 👉 • Integral formulas for ...
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#calculus #bprpcalculus #apcalculus #tutorial #math

Пікірлер: 45

@bprpcalculusbasics 2 ай бұрын

Check out the volume of a cone proof 👉 kzfaq.info/get/bejne/mtigq71ixuDYh3k.html

@falcon3548 2 ай бұрын

can you do more calculus proofs please? I am a geometry student and this is very interesting.

@AncientBulldozer 2 ай бұрын

I literally watched your previous video yesterday and in the morning I used the volume method you taught to derive the sphere volume and by sheer coincidence youve uploaded this video today 😂

@flowingafterglow629 2 ай бұрын

These types of "rotate around the axis" volume calculations were probably my favorite part of Calculus II I remember when were learning geometry volumes in 4th grade and we got to the volume of the cone = (1/3)*pi*r^2*h and I asked, how do we know that it is 1/3 of a cylinder? The teacher gave a good answer of, maybe you fill it with sand and see that it takes three of them to fill the cylinder, which is empirically ok, but I was very happy when I got to Calc II and could derive it analytically. I finally got my question answered exactly.

@brendanward2991 2 ай бұрын

That was so satisfying.

@BleuSquid 2 ай бұрын

I love the Tau vs Pi argument because it's fun to think about... but it was the comparison of the derivation of the volume of a sphere, to other well known equations that come to us through integration, that made me a believer in Tau.

@Sg190th 2 ай бұрын

Now we need the same with a circle and circumference.

@RadhakrishnanNair-zn8vh Ай бұрын

Great interpretation...Sir...Thank You very much...

@sinekavi 2 ай бұрын

Were you able to solve the integral @bprp calculus basics?

@JakkAuburn 2 ай бұрын

Is it possible to derive the formula for the surface area of a sphere in the same way? Just instead of calculating the area of the entire slice of a semi-circle, we calculate the length of the hypotenuse of triangles which we then make progressively more narrow so they end up giving us the arclength of the semi-circle?

@professorsogol5824 Ай бұрын

What is the curvature?? Is it measured in degrees or radians? Is it the radius of the circle that has its center on a line perpendicular to the tangent of the curve at the specified point?

@SokomoKudiomi-h6l 24 күн бұрын

I feel like I'm looking at a beautiful artwork without understand total of his beauty. But I want someday understand

@mehmetali4626 2 ай бұрын

next time could you make video for solve sphere volume with jacobian matrix ?

@Upward3D 2 ай бұрын

Nice.

@user-ei6rd7ei7x 2 ай бұрын

The sphere coordinates are here: x = t cos(u) cos(v) y = t cos(u) sin(v) z = t sin(u) -pi/2

@Ninja20704 2 ай бұрын

Can this be done without calculus though, I wonder. When I asked my calculus teacher they said that this wasn’t the first/original way they came up with the formula, so I have been wondering how you could prove it without calculus.

@hrayz 2 ай бұрын

Calculus, of this nature, is a short hand for a Limit Sum as ∆x->0

@gallentespeterjohn6543 2 ай бұрын

Cool!

@megumn6214 2 ай бұрын

in em field theory class we do this in spherical coordinates and I think it's easier to understand and visualize but you need to know vector algebra 🤓

@akuntumbal1485 2 ай бұрын

This is beautifull

@justinterrill2131 2 ай бұрын

Calculus now makes sense.

@Nobodyman181 2 ай бұрын

Pleeeeasseeee find Volume of 4th dimension sphere and 4d volume of 4d sphere 😢🙏🙏🙏

@happend 2 ай бұрын

I believe that volume is not the unit you mean, but the answer is the Integral from 0 to r of 2 * (4/3) * π * (√(r^2 - x^2))^3 dx.

@Nobodyman181 2 ай бұрын

@@happend thenk you

@happend 2 ай бұрын

@@Nobodyman181 I hope I've helped ^^

@hibosmo 2 ай бұрын

bro, why this pop up in my notifications? im getting PTSD from university calculus D:

@stefanmi1 2 ай бұрын

You're starting with the assumption that the formula for volume of a disk is known. Why not assume nothing and use polar coords? That's the way we learned it. And when you convert the Pythagorean formula to polar you get triple int of rho^2 * sin(phi) d(rho) d(theta) d(phi) with rho from 0 to r, theta from 0 to 2*pi, and phi from 0 to pi.

@hishamhamed5033 2 ай бұрын

That's the approach I'd take.

@rodrigocunha7828 27 күн бұрын

Share the link, please